Brighter galaxy bias: underestimating the velocity dispersions of galaxy clusters

We study the systematic bias introduced when selecting the spectroscopic redshifts of brighter cluster galaxies to estimate the velocity dispersion of galaxy clusters from both simulated and observational galaxy catalogues. We select clusters with N-gal >= 50 at five low-redshift snapshots from the publicly available De Lucia & Blaziot semi-analytic model galaxy catalogue. Clusters are also selected from the Tempel Sloan Digital Sky Survey Data Release 8 groups and clusters catalogue across the redshift range 0.021 < z < 0.098. We employ various selection techniques to explore whether the velocity dispersion bias is simply due to a lack of dynamical information or is the result of an underlying physical process occurring in the cluster, for example, dynamical friction experienced by the brighter cluster members. The velocity dispersions of the parent dark matter (DM) haloes are compared to the galaxy cluster dispersions and the stacked distribution of DM particle velocities is examined alongside the corresponding galaxy velocity distribution. We find a clear bias between the halo and the semi-analytic galaxy cluster velocity dispersion on the order of Sigma(gal)/Sigma(DM) similar to 0.87-0.95 and a distinct difference in the stacked galaxy and DM particle velocities distribution. We identify a systematic underestimation of the velocity dispersions when imposing increasing absolute I-band magnitude limits. This underestimation is enhanced when using only the brighter cluster members for dynamical analysis on the order of 5-35 per cent, indicating that dynamical friction is a serious source of bias when using galaxy velocities as tracers of the underlying gravitational potential. In contrast to the literature we find that the resulting bias is not only halo mass dependent but also that the nature of the dependence changes according to the galaxy selection strategy. We make a recommendation that, in the realistic case of limited availability of spectral observations, a strictly magnitude-limited sample should be avoided to ensure an unbiased estimate of the velocity dispersion.